Particle deposition from a natural convection flow onto a vertical isothermal flat plate

The deposition of particles from a laminar, natural convection boundary layer flow adjacent to a heated or cooled flat plate occurs due to a combination of thermophoretic drift and Brownian motion. In this paper, scale analysis is used to determine the magnitudes of the concentration boundary layer thickness and the normalized particle flux. Scaling arguments are also used to show that thermophoresis dominates Brownian motion in the concentration boundary layer whenever Le^(1/3)>(T∞/│ΔT│)^(1/2), where Le is the Lewis number of the particle and ΔT is the difference between the temperature of the plate surface and that of the air outside the momentum boundary layer (T_∞). Using a similarity transformation, the governing partial differential equations are converted to a system of ordinary differential equations which are solved numerically. Dimensionless particle flux is determined as a function of particle diameter in the range 0.001–3.0 μm and ΔT from −10 to 10 K. The results have application in understanding and preventing the soiling of indoor surfaces, including works of art